Drag S and T anywhere. The point M always sits exactly halfway between them. Watch the working below change as you move the points, and the two halves of the segment stay equal.
Drag S or TM moves on its ownTry dragging S and T across the origin
Both halves stay equal however you drag the points.
The three points
S
(-6, 2)
T
(4, 6)
M · the midpoint
(-1, 4)
Halves match
S to M
5.39
M to T
5.39
S to T · the whole segment
10.77
These two halves stay equal no matter where you drag the points. That is what makes M the midpoint.
Show
P and Q cut the segment into three equal parts. Once you can see how M works, try predicting where P and Q must land.
Noescio